How do you beat the Toy Story space crane game on Poptropica?

The "space crane" game is part of the Toy Story ad-game that appeared on Poptropica in March, 2010, in conjunction with the Toy Story/Toy Story 2 DVD release.

To save Buzz Lightyear from Sid, you have 60 seconds to remove all 10 of the LGM's (Little Green Men) from the crane game, and then lift out Buzz. The rewards are a Squeeze Toy Alien costume, a Buzz Lightyear or Jenny costume, and a marching army men (mini-soldiers) effect.